Linear Programming

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What is Linear Programming?

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Linear Programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model. Its function and constraints are linear relationships.

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What are constraints in Linear Programming?

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Constraints are the restrictions or limitations on the variables in a linear programming problem, often expressed as inequalities.

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What does the objective function represent in Linear Programming?

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The objective function is the function that needs to be maximized or minimized in a linear programming problem, typically representing profit or cost.

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What is the feasible region in Linear Programming?

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The feasible region is the set of all possible points that satisfy the constraints of a linear programming problem, usually represented graphically.

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How do you represent constraints graphically?

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Constraints are represented graphically by drawing lines on a coordinate plane, where the area that satisfies all constraints is the feasible region.

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What is the significance of the corner points in the feasible region?

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Corner points (or vertices) of the feasible region are significant because the optimal solution to a linear programming problem occurs at one of these points.

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What is the graphical method in Linear Programming?

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The graphical method is a technique used to solve linear programming problems with two variables by graphing the constraints and identifying the feasible region.

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What is an inequality in the context of Linear Programming?

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An inequality is a mathematical expression that shows the relationship between two expressions that are not necessarily equal, often used to define constraints.

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What does the term 'bounded' mean in Linear Programming?

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A feasible region is bounded if it is enclosed and has a finite area; otherwise, it is unbounded.

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What is the role of the objective function in determining the optimal solution?

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The objective function is evaluated at each corner point of the feasible region to find the maximum or minimum value, determining the optimal solution.